Diaschismic family: Difference between revisions

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This extension of 5-limit diaschismic adds prime 17 and ~~which with respect to~~ [[MVP archagall~~]] is able to express the harmonics [[75/1|75]] and [[85/1|85~~]] in ~~their appropriate~~ prime subgroup~~. It achieves this~~ by equating [[85/64]] with [[4/3]] by tempering out their difference of [[256/255]] (S16). Therefore it also tempers out [[289/288]] (S17) and thus equates [[17/15]] with [[9/8]] due to tempering out [[136/135]] (S16⋅S17). It could be described as the 10 & 12 temperament with strong emphasis on 12edo being the better tuning on the 2.3.5.17 subgroup, implying ideal tunings of 34edo, 46edo or 80edo.

This extension of 5-limit diaschismic adds prime 17, and can be seen as the trivial tuning of [[MVP archagall]] in its minimal prime subgroup by equating [[85/64]] with [[4/3]] by tempering out their difference of [[256/255]] (S16). Therefore it also tempers out [[289/288]] (S17) and thus equates [[17/15]] with [[9/8]] due to tempering out [[136/135]] (S16⋅S17). It could be described as the 10 & 12 temperament with strong emphasis on 12edo being the better tuning on the 2.3.5.17 subgroup, implying ideal tunings of 34edo, 46edo or 80edo.

Subgroup: 2.3.5.17

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[[Category:Diaschismic family| ]]

[[Category:Diaschismic| ]]

[[Category:Temperament families]]

[[Category:Catalogs of rank-2 temperaments]]

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 {{See also | Fiventeen }}
-This extension of 5-limit diaschismic adds prime 17 and which with respect to [[MVP archagall]] is able to express the harmonics [[75/1|75]] and [[85/1|85]] in their appropriate prime subgroup. It achieves this by equating [[85/64]] with [[4/3]] by tempering out their difference of [[256/255]] (S16). Therefore it also tempers out [[289/288]] (S17) and thus equates [[17/15]] with [[9/8]] due to tempering out [[136/135]] (S16⋅S17). It could be described as the 10 & 12 temperament with strong emphasis on 12edo being the better tuning on the 2.3.5.17 subgroup, implying ideal tunings of 34edo, 46edo or 80edo.
+This extension of 5-limit diaschismic adds prime 17, and can be seen as the trivial tuning of [[MVP archagall]] in its minimal prime subgroup by equating [[85/64]] with [[4/3]] by tempering out their difference of [[256/255]] (S16). Therefore it also tempers out [[289/288]] (S17) and thus equates [[17/15]] with [[9/8]] due to tempering out [[136/135]] (S16⋅S17). It could be described as the 10 & 12 temperament with strong emphasis on 12edo being the better tuning on the 2.3.5.17 subgroup, implying ideal tunings of 34edo, 46edo or 80edo.
 Subgroup: 2.3.5.17
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 [[Category:Diaschismic family| ]] <!-- main article -->
+[[Category:Diaschismic| ]] <!-- key article -->
 [[Category:Temperament families]]
 [[Category:Catalogs of rank-2 temperaments]]

Diaschismic family: Difference between revisions

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